I got a better coach but i still cannot train my players further

You should look for a better "Basic" trainer to start with.

Indeed, there are several types of coaches and each type has his own set of exercises. Your team's default coach is a "Basic" coach and unlocks an exercise for each ability. The other types of coaches ("Technique", "Physique", etc.) do not improve the default exercises but unlock new ones. See "How to unlock new exercises" for more information.

Why have players disappeared from the training page?

There are several possible reasons:

- Players are injured: select the "Injured players" tab to view them. You can heal them with crutches and bandages in the gear section.
- Players are depressed: they can be viewed on the "Injured players" tab. You can improve their mental with massages in the gear section.